Struct Arc 

pub struct Arc<T> {
    pub s: V<T>,
    pub e: V<T>,
    pub half: T,
}

A circular arc from s to e, turning counter-clockwise by 2 * half (clockwise if negative).

Fields

s: V<T>

e: V<T>

half: T

Implementations

impl<T: Scalar> Arc<T>

pub fn chord(&self) -> V<T>

pub fn chord_length(&self) -> GeopResult<T>

pub fn chord_mid(&self) -> V<T>

pub fn left(&self) -> GeopResult<V<T>>

Unit normal to the chord, pointing to its left: the side the center is on for a counter-clockwise minor arc.

pub fn curvature(&self) -> GeopResult<T>

pub fn radius(&self) -> GeopResult<T>

|radius|. Infinite for a straight arc.

pub fn center(&self) -> GeopResult<V<T>>

Center: chord_mid + left * (L / 2) cot(half). Infinitely far for a straight arc, so only for constraints that are meaningless there anyway (concentricity, tangency to a circle).

pub fn arc_mid(&self) -> GeopResult<V<T>>

The point halfway along the arc: chord_mid - left * (L / 2) tan(half / 2).

pub fn circle_residual(&self, p: V<T>) -> GeopResult<T>

Signed distance-like residual of p against the arc’s full circle, finite and smooth for every half including a straight arc.

With q = p - chord_mid, the circle is |q|^2 - 2 d (left . q) - L^2/4 = 0 for d the center’s offset along left. Multiplying by the curvature k (and using k d = cos(half)) gives G = k |q|^2 - 2 cos(half) (left . q) - k L^2 / 4, which is a line’s equation at k = 0. Near the circle G ≈ ±2 dist, so G / 2 is a distance.

pub fn tangent_start(&self) -> GeopResult<V<T>>

Unit tangent at s, in the direction of travel.

pub fn tangent_end(&self) -> GeopResult<V<T>>

Unit tangent at e, in the direction of travel.

pub fn length(&self) -> GeopResult<T>

Arc length L * half / sin(half).

Trait Implementations

impl<T: Clone> Clone for Arc<T>

fn clone(&self) -> Arc<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Copy> Copy for Arc<T>

impl<T: Debug> Debug for Arc<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.